For example: College GPA Increase Decrease No Change Increase Decrease Change in Time Comparison of Road Work Funds of New York and California 1990–1995 New York California KEY 0 10 20
Trang 1Broken-Line Graphs
Broken-line graphs illustrate a measurable change over time If a line is slanted up, it represents an increase whereas
a line sloping down represents a decrease A flat line indicates no change as time elapses
Scatterplots illustrate the relationship between two quantitative variables Typically, the values of the
inde-pendent variables are the x-coordinates, and the values of the deinde-pendent variables are the y-coordinates When
presented with a scatterplot, look for a trend Is there a line that the points seem to cluster around? For example:
College GPA
Increase
Decrease
No Change
Increase Decrease
Change in Time
Comparison of Road Work Funds
of New York and California
1990–1995
New York
California
KEY
0
10
20
30
40
50
60
70
80
90
Year
Trang 2In the previous scatterplot, notice that a “line of best fit” can be created:
Practice Question
Based on the graph above, which of the following statements are true?
I In the first hour, Vanessa sold the most lemonade.
II In the second hour, Lupe didn’t sell any lemonade.
III In the third hour, James sold twice as much lemonade as Vanessa.
a I only
b II only
c I and II
d I and III
e I, II, and III
Answer
d Let’s evaluate the three statements:
Statement I: In the first hour, Vanessa sold the most lemonade.
In the graph, Vanessa’s bar for the first hour is highest, which means she sold the most lemonade in the first hour Therefore, statement I is TRUE
Statement II: In the second hour, Lupe didn’t sell any lemonade.
Lemonade Sold
Vanessa James Lupe
0
2
4
6
8
10
12
14
16
College GPA
6 5
Trang 3In the second hour, there is no bar for James, which means he sold no lemonade However, the bar for Lupe is at 2, so Lupe sold 2 cups of lemonade Therefore, statement II is FALSE
Statement III: In the third hour, James sold twice as much lemonade as Vanessa.
In the third hour, James’s bar is at 8 and Vanessa’s bar is at 4, which means James sold twice as much lemonade as Vanessa Therefore, statement III is TRUE
Answer: Only statements I and III are true
Matrices are rectangular arrays of numbers Below is an example of a 2 by 2 matrix:
Review the following basic rules for performing operations on 2 by 2 matrices
Addition
Subtraction
Multiplication
Scalar Multiplication
k
a1 a2
a3 a4
=
ka1 ka2
ka3 ka4
a1 a2
a3 a4
×
b1 b2
b3 b4
=
a1b1+ a2b3 a1b2+ a2b4
a3b1+ a4b3 a3b2+ a4b4
a1 a2
a3 a4
−
b1 b2
b3 b4
=
a1− b1 a2− b2
a3− b3 a4− b4
a1 a2
a3 a4
+
b1 b2
b3 b4
=
a1+ b1 a2+ b2
a3+ b3 a4+ b4
a1 a2
a3 a4
Trang 4
Practice Question
Which of the following shows the correct solution to the problem above?
a.
b.
c.
d.
e.
Answer
e.
+
=
4+ 6 3 + 2
7+ 5 1 + 2
=
10 5
12 3
10 5
12 3
24 6
35 2
−2 1
11 11
+
=
6 7
Trang 6E q u a t i o n s
To solve an algebraic equation with one variable, find the value of the unknown variable.
Rules for Working with Equations
1 The equal sign separates an equation into two sides.
2 Whenever an operation is performed on one side, the same operation must be performed on the
other side
3 To solve an equation, first move all of the variables to one side and all of the numbers to the other Then
simplify until only one variable (with a coefficient of 1) remains on one side and one number remains on the other side
C H A P T E R
Algebra Review
This chapter reviews key skills and concepts of algebra that you need
to know for the SAT Throughout the chapter are sample questions in the style of SAT questions Each sample SAT question is followed by
an explanation of the correct answer
6
6 9